In a Boiling Water nuclear Reactor there are basically three modes of heat transfer that must be considered in defining thermal limits for the reactor: (i) Nucleate boiling, (ii) transition boiling and (iii) film boiling. Nucleate boiling is the preferred efficient mode of heat transfer in which the BWR is designed to operate. Transition boiling is manifested by an unstable fuel rod cladding surface temperature which rises suddenly as steam blanketing of the heat transfer surface occurs, then drops to the nucleate boiling temperature as the steam blanket is swept away by the coolant flow, then rises again. At still higher fuel rod/bundle operating powers, film boiling occurs which results in higher fuel rod cladding temperatures. The cladding temperature in film boiling, and possibly the temperature peaks in transition boiling, may reach values which could cause weakening of the rod cladding and accelerated corrosion. Thus, fuel rod overheating is conservatively defined as the onset of the transition from nucleate boiling to film boiling. Accordingly, the conventional basis for reactor core and fuel rod design is defined such that some "margin", accommodating various design and operational "uncertainties", is maintained between the most limiting operating condition and the transition boiling condition at all times for the life of the core.
The onset of transition boiling can be predicted by a correlation to the steam quality at which boiling transition occurs--called the "critical quality". Steam quality can be readily measured and is generally a function of measuring distance above the boiling boundary (boiling length) for any given mass flow rate, power level, pressure and bundle flow geometry among other factors. A "critical power" is defined as that bundle power which would produce the critical quality of steam. Accordingly, a "critical power ratio" (CPR) is then defined as the ratio of the critical power to the bundle operating power at the reactor condition of interest and is descriptive the relationship between normal operating conditions and conditions which produce a boiling transition. Consequently, the CPR is conventionally used as the figure of merit for rating reactor design and operation. To assure a safe and efficient operation of the reactor, the CPR must be kept above a prescribed value for all of fuel assemblies in the core. Consequently, reactor operating limits are conventionally defined in terms of the most limiting fuel assembly in the core--defined as the "minimum critical power ratio" (MCPR). Reactor operating limits are thus often stated in terms of MCPR.
In nuclear power generation engineering, it is widely recognized that there is a possibility, however small, that the occurrence of a reactor transient event combined with the various "uncertainties" and tolerances inherent in reactor design and operation may cause transition boiling to exist locally for some period of time. Accordingly, MCPR operating limits are conventionally set in accordance with the United States Nuclear Regulatory Commission (USNRC) design basis requirement that transients caused by single operator error or single equipment malfunction shall be limited such that, taking into consideration uncertainties in the core operating state, more than 99.9% of the fuel rods are expected to avoid boiling transition. Accordingly, a safety limit minimum critical power ratio (SLMCPR) is defined under current USNRC requirements as the MCPR where no more than 0. 1% of the fuel rods are subject to boiling transition.
Notwithstanding the above design basis requirements, developments in fuel design, core loading, and reactor operation over the past years have gradually increased the operating limit minimum critical power ratio (OLMCPR) and reduced the operational "margin" conventionally associated with Boiling Water Reactors (BWRs). Several factors have contributed to the reduction in reactor operational margin. For example, the development of 9-by-9 and 10-by-10 fuel rod bundles having smaller rod diameters has reduced the thermal time constant associated with the fuel rods and made the fuel rods more sensitive to power transients. In addition, the conventional use of a "one-dimensional" power shape model in the mathematical modeling and analysis of the transient response of fuel rods has the effect of further reducing the calculated operating margin. As a result, the OLMCPR has increased to within a range of 1.3 to 1.4--which for most BWRs is typically set from an observance of "fast" pressurization transients (e.g., such as those resulting from a turbine "trip" without bypass). However, contemporary movements toward the use of high energy cores--characterized by power up-rates, long cycles and high capacity factors--necessitates increased critical power ratio (CPR) margins in order to optimize the fuel cycle economy. Moreover, as a result of contemporary optimizations in fuel bundle design, recent increases in operational safety limits translate into a corresponding increase in the operating limit CPR.
Motivated by these and other concerns, the inventors of the present invention were led to examine more closely some of the processes conventionally used in evaluating BWR designs and calculating OLMCPR. As a consequence, it was realized that the conventional processes were laden with excessive conservatism that resulted in inaccurate evaluations of reactor performance and calculation of the OLMCPR. For example, the following is a brief list summarizing five of the somewhat more prominent factors identified by the inventors as contributing to excessive conservatism in conventional BWR performance evaluations:
i. The use of one-dimensional (1-D) instead of three-dimensional (3-D) methods. PA1 ii. The inconsistent use of radial power shapes. PA1 iii. The addition of "uncertainties" instead of a statistical combination. PA1 iv. A failure to consider direct moderator heating in the correlation for boiling transition. PA1 v. Overly conservative safety limit parameters.
The conventional 1-Dimensional modeling methods used for evaluation of transients fail to incorporate the "flattening" of the shape of the radial power distribution that generally occurs during a transient --thus leading to an over prediction of the transient change in critical power ratio (DCPR). PA2 The safety limit is calculated in 3-D using the flattest possible steady state radial power shape in order to maximize the number of rods close to boiling transition. Conventionally, the transient CPR (DCPR) is calculated in 1-D assuming a highly peaked radial power shape in order to drive the bundle to the safety limit. If the same peaked radial power shape that was used for the DCPR evaluation is used for the safety limit, a lower safety limit would result. Conversely, if the same flattened radial power shape used for the safety limit were applied to the transient the DCPR would be reduced. For either situation the OLMCPR would be reduced and operating margin would be increased. PA2 Values representing uncertainties in the calculations for both safety limit and DCPR are currently added linearly. Since the parameters contributing to these "uncertainties" are statistically independent, a "propagation of error" or equivalent method is a more appropriate approach for combining these values. PA2 In an actual fuel bundle, a small fraction of the energy is deposited directly into the fluid. However, in conventional fuel rod modeling for a test bundle, all power is considered as residing entirely in the fuel rods. PA2 Smaller values for "uncertainties" than those conventionally used can be justified--resulting in a lower safety limit.
Conventionally, a SLMCPR has been statistically evaluated by using steady state calculations. (See for example, the General Electric publication General Electric BWR Thermal Analysis Basis (GETAB): Data, Correlation and Design Application, NEDO-10958-A, January 1977). A statistical evaluation process similar to the one described in this publication was used in the safety evaluation of the licensing topical report for conventional one-dimensional simulation methods, but was only applied to the evaluation of the transient DCPR. (See the General Electric Publication Qualification of the One-dimensional Core Transient Model for Boiling Water Reactors (Volume 1), NEDE-24154-A, Class I, August 1988).
Based on the above considerations, the inventors of the present invention realized that due to the excessive degree of conservatism inherent in the conventional basis used for evaluation of BWR operations, a substantial increase in the operating margin for a BWR could be realized by using a less conservative approach toward determining the OLMCPR--as long as such an approach could be demonstrated as mathematically sound. A resultant benefit is that any substantial increase in the permissible operating margin for a reactor translates into increased operating efficiency, greater fuel generation and/or lowered fuel exhaustion. For example, demonstrating that a particular reactor or reactor design actually has a greater operational margin than may have been previously realized--for example, due to the use of an unnecessarily overly conservative evaluation method--could permit operation at increased output power levels or at comparable power output levels using less fuel. Accordingly, a less conservative and more mathematically sound evaluation method that results in a substantially greater operational margin for Boiling Water Reactors is presented herein for calculating and demonstrating the OLMCPR. Moreover, in principle, the improved method and system of the present invention may also be applied toward the statistical determination of operating limits for other reactor parameters important to reactor safety, for example, the limiting linear heat generation rate (LHGR) in a BWR, the critical heat flux limit in a PWR or LMCR, or the maximum fuel temperature, or the maximum fuel cladding temperature limit in any reactor containing fuel enclosed by a metallic material. These other applications would require that the probability distribution be characterized for each parameter of interest either in the form of a histogram or by some other means such as the generation of a response surface.
Briefly, the improved method of the present invention is based on producing a histogram of the number of reactor fuel rods susceptible to operation at "boiling transition" temperatures over a range of variations in selected parametric quantities that are indicative of reactor design constraints and operating conditions. In addition, a core operational modeling approach using multi-dimensional analysis is employed for simulating BWR thermal hydraulics and neutron kinetics during an "anticipated operational occurrence"or AOO in the reactor (for example, a operational occurrence that causes a brief power transient). Basically, in the present invention, all model and reactor plant parameters that may affect the number of rods subject to boiling transition (NRSBT) are first evaluated simultaneously using multi-dimensional modeling of a plurality of fuel rods during a reactor transient condition. The NRSBT is then evaluated statistically in order to determine the OLMCPR directly without the need for first calculating a value for the SLMCPR. Using this approach, the present invention achieves a direct evaluation of OLMCPR of the reactor from a statistical analysis of histograms for the transient condition--as opposed the conventional "indirect" approach of determining an OLMCPR from a combination of values obtained by separately evaluating both a steady state Safety Limit Minimum Critical Power Ratio (SLMCPR) and the change in the critical power ratio (DCPR) due to a transient operational occurrence.
Although the use of statistical processes for the evaluation of the "uncertainties" in the modeling of peak cladding temperature for a loss-of-coolant accident has been previously proposed and published by the United States Nuclear Regulatory Commission (USNRC) (See for example, Quantifying Reactor Safety Margin, Application of Code Scaling, Applicability, and Uncertainty Evaluation Methodology to a Large Break Loss-of-Coolant Accident, NUREG/CR-5249, October 1989 and U.S. Nuclear Regulatory Commission, Regulatory Guide 1.157, Best-Estimate Calculations of Emergency Core Cooling System Performance, May 1989), these publications do not define how component uncertainties can be ultimately combined nor how the resulting total uncertainties are to be applied. Moreover, none of the above publications describe or suggest a direct statistical evaluation of the NRSBT during the transient.